## Creating moment function for a 2D frame

## Creating moment function for a 2D frame

(OP)

Hi there,

I am trying to solve a rigid frame that is supported by two pin supports. I am doing this using the unit load (or virtual work) method. To do this I am trying to create moment functions for each segement of the frame.

This is what my frame looks like:

I have replaced the pin support at node 1 to a roller (which is what my text book said to do).

The virtual structure looks like the following:

For segment 2:3 I am attempting to create a moment function. I can do this easily with a beam in one dimension. However, because this is a frame I need to take the momenmt function in two directions.

The formula for virtual work across sgement 2:3 is:

Where 'M' is the moment fuction of the real structure and 'm' is the moment function for the virtual structure.

Thus, I have created the moment function to be:

From here, I have tried solving this using the double inegral procedure, but I am not getting the correct result. Am I on the right path here, or am I wqay off?

I am trying to solve a rigid frame that is supported by two pin supports. I am doing this using the unit load (or virtual work) method. To do this I am trying to create moment functions for each segement of the frame.

This is what my frame looks like:

I have replaced the pin support at node 1 to a roller (which is what my text book said to do).

The virtual structure looks like the following:

For segment 2:3 I am attempting to create a moment function. I can do this easily with a beam in one dimension. However, because this is a frame I need to take the momenmt function in two directions.

The formula for virtual work across sgement 2:3 is:

Where 'M' is the moment fuction of the real structure and 'm' is the moment function for the virtual structure.

Thus, I have created the moment function to be:

From here, I have tried solving this using the double inegral procedure, but I am not getting the correct result. Am I on the right path here, or am I wqay off?

## RE: Creating moment function for a 2D frame

Your vertical reactions are wrong ... you need to include the overturning moments from the horizontal loads,

and this'll show you the additional moments in member 2.

Re-read your post. So this is a redundant structure, pinned at 1 and 3. So you're using virtual work to final the horizontal reaction at 1 (the redundancy).

So yes, release the constraint (as you have) and apply a unit load. But you need to consider all three elements of the frame.

Draw the FBDs, it'll give you some clarity on the problem.

If still in doubt, look for a worked solution ... there are many around.

"Hoffen wir mal, dass alles gut geht !"

General Paulus, Nov 1942, outside Stalingrad after the launch of Operation Uranus.

## RE: Creating moment function for a 2D frame

By moment function I mean the equation you construct to find the moment at anywhere along the length of the member 'x'.

If I were just constructing the equation along member 2:3 the equation would be 5.1667*x - 24*(x-3). However, this is a frame with 2 dimensions, so I have added the dimension 'y'. For the virtual work procedure you solve the integral of the moment equation of the real structure 'M' multiplied by the virtual moment equation 'm'. Thus, 'M' equals 5.1667*x - 24*(x-3), and 'm' equals 1*y. The emphasis of my question here is I have I dont this correctly? Because I have an inegral with two independant variables which I have never tackled before till now.

I know you have to consider all three elements of the frame. Member 1:2 equals zeros. I am on member 2:3 and will next solve member 3:4

Sorry for the confusion.

Many thanks

## RE: Creating moment function for a 2D frame

## RE: Creating moment function for a 2D frame

_{1-2}; but your M(x) is not correct, as your ground reactions are not correct ... unless you are only solving for the vertical load.I'm not sure what solving for member 2-3 in isolation gets you ? Sure, in member 1-2 there is no M ('cause there is no transverse shear, at 1 or anywhere) ... 1-2 is axially loaded only. But 3-4 does have a moment, both M and m, so it'll be part of the solution. But then you say you'll move onto 3-4 once you've done 2-3, so ok.

"Hoffen wir mal, dass alles gut geht !"

General Paulus, Nov 1942, outside Stalingrad after the launch of Operation Uranus.

## RE: Creating moment function for a 2D frame

The equation for Member 2 is not correct. It should be M = V1*x - 24(x>3)(x-3). The term (x>3) is a Boolean expression; when x is less than 3, it is zero. If you don't include the boolean expression you won't get the right answer.

And by the way, it would be helpful if you put some dimensions on your sketch. We are good, but we're not mind readers.

## RE: Creating moment function for a 2D frame

"Hoffen wir mal, dass alles gut geht !"

General Paulus, Nov 1942, outside Stalingrad after the launch of Operation Uranus.

## RE: Creating moment function for a 2D frame

## RE: Creating moment function for a 2D frame

## RE: Creating moment function for a 2D frame

## RE: Creating moment function for a 2D frame

but your reactions aren't correct ? The posted drawing is not a free body. So the moment in 2-3 will be different ...

"Hoffen wir mal, dass alles gut geht !"

General Paulus, Nov 1942, outside Stalingrad after the launch of Operation Uranus.

## RE: Creating moment function for a 2D frame

The reaction at the left support appears to be correct, i.e. V

_{1}=5.1667, H_{1}=0 for the determinate structure where the pinned support is changed to a roller.## RE: Creating moment function for a 2D frame

General Paulus, Nov 1942, outside Stalingrad after the launch of Operation Uranus.

## RE: Creating moment function for a 2D frame

_{1}using scaled dimensions. They are shown on the sketch below:Dimensions a, b and L are 3, 6 and 9m respectively. We still don't know dimensions c and d, although it appears they are probably 5 and 2.5m.

Overturning moment = 12*5+15*2.5 = 97.5kN-m

Stabilizing moment = 24*6 = 144kN-m

V1 = (144-97.5)/9 = 5.1667kN

## RE: Creating moment function for a 2D frame

sorry

General Paulus, Nov 1942, outside Stalingrad after the launch of Operation Uranus.

## RE: Creating moment function for a 2D frame